Please solve question 14

Please solve question 14 11. 12. 13. 14. Find all possible values off(: Solve Solve Solve 4 4 x 15. Solve 2 16. Solve

Dear student,
$$\begin{gathered} 4^{-x+.5}-7.2^{-x}<4 \\ {\left(2^2\right)}^{\left(-x+.5\right)}-7\times 2^{-x}<4 \\ {2}^{-2x+1}-7\times 2^{-x}<4 \\ 2\times {\left(2^{-x}\right)}^2-7\times 2^{-x}<4 \\ let 2^{-x} =t \\ 2t^2-7t-4<0 \\ 2t^2-8t+t-4<0 \\ 2\left(t-4\right)+1\left(t-4\right)<0 \\ \left(t-4\right)\left(2t+1\right)<0 \\ 2\left(t-4\right)\left(t+\frac{1}{2}\right)<0 \\ -\frac{1}{2}<t<4 \\ we know t>0 \\ 0<t<4 \\ 0<2^{-x}<4 \\ -2<x<0 \\ answer \end{gathered}$$
Hope this information will clear your doubts. If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible.
Regards